Analysis of the wave propagation in complicated shielded waveguides with inclusions constitutes an important class of vector electromagnetic problems. There has been an increasing interest during the last 10–15 years to study the processes of electromagnetic wave propagation in guiding systems with nonhomogeneous filling. Although different types of them are widely used in various practical applications for more than 30 years, and a lot of their physical properties have been established the interest in developing rigorous mathematical technique in this field of electromagnetics remains. A main reason is the wide application of modern guiding systems such as microstrip and slot transmission lines, which produces new types of problems to be solved numerically and requires elaborating specific methods of the spectral theory of (OVFs) and (OPs).